Electron state density in short-range-disordered chains

A perturbation treatment of short-range disorder in a linear chain with weak wells is given for energies lying within the Bragg reflection region, and the resulting state density curves compared with Monte Carlo computer calculations. When a correction is introduced for the error intrinsic to the weak-binding method, present even in the case of a perfect lattice, the disorder is found to be adequately taken into account simply by a reduction in the effective well strength. This investigation arose from consideration of eigenstates of long-range-disordered chains and will find application in a determination of the state density and the range of localization of such states.